Engineering Board Exam Reviewer · Nonhomogeneous Second-Order Equations · medium

Solve y''+y=2 with y(0)=0 and y'(0)=0, and find y(π).

1. 0
2. 2
3. 4
4. -2

Answer

C. 4

Solution

yc=C1 x+C2 x and yp=2. So y=2+C1 x+C2 x. y(0)=0 C1=-2; y'(0)=0 C2=0. Thus y=2-2 x and y(π)=2-2(-1)=4.

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